Teleparallel gravity and dimensional reductions of noncommutative gauge theory

We study dimensional reductions of noncommutative electrodynamics on flat space, which lead to gauge theories of gravitation. For a general class of such reductions, we show that the noncommutative gauge fields naturally yield a Weitzenböck geometry on spacetime and that the induced diffeomorphism invariant field theory can be made equivalent to a teleparallel formulation of gravity which macroscopically describes general relativity. The Planck length is determined in this setting by the Yang-Mills coupling constant and the non-commutativity scale. The effective field theory can also contain higher curvature and non-local terms which are characteristic of string theory. Some applications to D-brane dynamics and generalizations to include the coupling of ordinary Yang-Mills theory to gravity are also described. ©2001 The American Physical Society.